Circle A has a radius of 2  and a center of (8 ,6 ). Circle B has a radius of 3  and a center of (2 ,3 ). If circle B is translated by <-1 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Apr 9, 2016

no overlap , d ≈ 2.07

Explanation:

A translation does not change the shape of a figure , only it's position.

Under a translation of $\left(\begin{matrix}- 1 \\ 2\end{matrix}\right)$

centre of circle B (2 , 3 ) → (2 -1 , 3 + 2) → (1 , 5)

Now, require to calculate the distance between the centres of A and B , using the $\textcolor{b l u e}{\text{ distance formula }}$

 d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2

where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(8 , 6\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 5\right)$

d = sqrt((1-8)^2 + (5-6)^2) = sqrt(49 + 1) = sqrt50 ≈ 7.07

now, radius of A + radius of B = 2 + 3 = 5

Since sum of radii < distance between centres , no overlap.

and distance (d) between circles = 7.07 - 5 = 2.07